> Intuitively?! Oh, I see how I must have been misleading. I suppose I
> should have used a different syntax than what I used. But
> mathematically what is lim_{x,y->oo} x-y ? My impression is that if
> the order of the limit matters I would expect "undefined" as an
> answer. My intuition says that there isn't one variable going to
> infinity faster. If you assume one does, then you assume a particular
> answer.
The following are three different mathematical concepts:
lim(lim(f(x,y), x, oo), y, oo)
lim(lim(f(x,y), y, oo), x, oo)
lim_{x, y \to oo} f(x,y) <-- sympy does not have an expression for
this, and it wouldn't be implemented anyway
As you have just discovered, in general these need not be the same
(and in fact you can even cook up examples where all limits involved
are finite).
>
> Also, f(x,y)=x-y isn't singular.
>
> --
> Julien
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